Andrea Barzagli had gifted Inter the lead in the second half when he turned a cross into his own net but Juventus hit back with two goals in two minutes to put themselves in front again.
Cuadrado made an intelligent run down the right-side of the box and saw his cross take a deflection off Milan Skriniar to wrong-foot opposing goalkeeper Samir Handanovic and hit the back of the net.
The visitors made it 3-2 minutes later after Higuain headed home a fierce free-kick from the left wing.
Cuadrado (87'):
28 April 2018
Higuain (89'):
28 April 2018